Question

Suppose a researcher wanted to know the sample size needed at the 99.74% confidence level for a pharmaceutical drug study in which the variability of the population is unknown and the acceptable margin of error is 1%. Calculate the sample size needed.

Answer 1

Given that, margin of error ( E ) = 0.01

proportion is unknown so we assume p = 0.5

confidence level = 99.74% ( c = 0.9974)

significance level = 1 - 0.9974 = 0.0026

0.9974 + 0.0013 = 0.9987

Using standard normal z-table we get, z-score corresponding probability 0.9974 is Z = 3.00

Z-critical value is,

We want to find, the sample size ( n )

n = 22500

Required sample size = 22500